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# 2.1: Properties of Rational Numbers

Difficulty Level: Basic Created by: CK-12
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Equivalent Fractions

Equivalent fractions are fractions that can each be simplified to the same fraction. An equivalent fraction is created by multiplying both the numerator and denominator of the original fraction by the same number.

improper fractions

These are rational numbers where the numerator is greater than the denominator. Improper fractions can be rewritten as a mixed number – an integer plus a proper fraction. An improper fraction represents a number greater than one.

proper fractions

Rational numbers where the numerator is less than the denominator. A proper fraction represents a number less than one.

rational number

A rational number is a number that can be expressed as the quotient of two integers, with the denominator not equal to zero.

common denominator

The common denominator is the least common multiple of the denominators of multiple fractions. Each fraction can be rewritten as an equivalent fraction using the common denominator.

Denominator

The denominator of a fraction (rational number) is the number on the bottom and indicates the total number of equal parts in the whole or the group. $\frac{5}{8}$ has denominator $8$.

Irrational Number

An irrational number is a number that can not be expressed exactly as the quotient of two integers.

Least Common Denominator

The least common denominator or lowest common denominator of two fractions is the smallest number that is a multiple of both of the original denominators.

Least Common Multiple

The least common multiple of two numbers is the smallest number that is a multiple of both of the original numbers.

Lowest Common Denominator

The lowest common denominator of multiple fractions is the least common multiple of all of the related denominators.

Mixed Number

A mixed number is a number made up of a whole number and a fraction, such as $4\frac{3}{5}$.

Numerator

The numerator is the number above the fraction bar in a fraction.

proper fraction

A proper fraction has a numerator that is a lesser absolute value than the denominator. Proper fractions always represent values between -1 and 1.

reduce

To reduce a fraction means to rewrite the fraction so that it has no common factors between numerator and denominator.

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